Description

The Josephs problem is notoriously known. For those who are not familiar with the problem, among n people numbered 1, 2, . . . , n, standing in circle every mth is going to be executed and only the life of the last remaining person will be saved. Joseph was smart enough to choose the position of the last remaining person, thus saving his life to give the message about the incident.

The persons are eliminated in a very peculiar order; m is a dynamical variable, which each time takes a different value corresponding to the Fibonacci numbers succession (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...). So in order to kill the i-th person, Josephus counts up to the i-th Fibonacci number.

For example, there are 6 people in a circle, and the sequence of counting is Fibonacci number succession (1, 1, 2, 3, 5 …).

In the beginning, the step to kill m = 1. The sequence of killing people is as follows.

1.............................(kill 1, and m is changed to 1)

2.............................(kill 2, and m is changed to 2)

3, 4.........................(kill 4 ,and m is changed to 3)

5, 6, 3.....................(kill 3 ,and m is changed to 5)

5, 6, 5, 6, 5.............(kill 5)

Then print 6 as answer.

 

Let’s solve this problem using C++. You have been provided with the following class definitions:

 

class Node

{

   friend class Josephus;

   public:

        Node():next( NULL ){

        }

          Node( const int &info ) //constructor

      :number( info ), next( NULL )

      {

      } //end ListNode constructor

   private:

          Node *next;

        int number;

};//end class Node

 

class Josephus

{

    public:

         Josephus();

         ~Josephus();

         Josephus(const int &);

         int kill(); // return the survival’s position

 

    private:

        void generatecircularlinkedList(const int &); // generate circular linked-list

        void generateFib(const int &); // generate a Fibonacci sequence table

        int sequence[50]; // store Fibonacci number

        int noOfPeople;

        Node *head;

};

 

REQUIREMENTS:

In this practice, you are asked to implement the following member functions:

Josephus class:

• constructor
• destructor
• int kill();
• void generatecircularlinkedList(const int &);
• void generateFib(const int &);

Note:

1.This problem involves three files.

• function.h: Class definitions.
• function.cpp: Member-function definitions.
• main.cpp: A driver program to test your class implementation.

You will be provided with main.cpp and function.h, and asked to implement function.cpp.

function.h

#ifndef FUNCTION_H #define FUNCTION_H #include <iostream> class Node { friend class Josephus; public: Node():next( NULL ){ } Node( const int &info ) //constructor :number( info ), next( NULL ) { } //end ListNode constructor private: Node *next; int number; };//end class Node class Josephus { public: Josephus(); ~Josephus(); Josephus(const int &); int kill(); // return the survival’s position private: void generatecircularlinkedList(const int &); // generate circular linked-list void generateFib(const int &); // generate a Fibonacci sequence table int sequence[50]; // store Fibonacci number int noOfPeople; Node *head; }; #endif // FUNCTION_H

main.cpp

#include <iostream> #include "function.h" using namespace std; int main(){ int numofpeople; while(cin>>numofpeople){ Josephus Jose(numofpeople); int survival = Jose.kill(); cout<<survival<<endl; } }

2.For OJ submission:

       Step 1. Submit only your function.cpp into the submission block.

       Step 2. Check the results and debug your program if necessary.

Input

Each line contains a number n<=45, which is the number of people. Input is terminated by EOF.

Output

The output will consist in separate lines containing the position of the person which life will be saved.

Sample Input  Download

Sample Output  Download

Partial Judge Code

10996.cpp

Partial Judge Header

10996.h

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